In most circuits, we can assume that resistance is constant in relation to current and voltage. This linear relation can be graphically shown in figure 1.

Fig.1: Plot of Linear Relation between Current and Voltage

For example, if 3V is applied to a certain resistor and 1A flows, then 6V applied to the same resistor will cause double the current, or 2A, to flow.

**Nonlinear Resistance**

The property exhibited by devices whose resistance does not change uniformly with changes in voltage or current.

Many different devices have characteristic curves (I-V plots) that are not straight lines, and they are, therefore, not linear devices. Such devices are called nonlinear devices since their resistances are nonlinear resistances.

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Typical nonlinear devices are the filament of an incandescent lamp, diode, thermistor, and varistor (a special resistor made of Carborundum crystals held together by a binder). The curve in figure 2 shows how the current through a varistor increases very rapidly when the voltage across the device increases beyond a certain amount (about 100 V in this case). A corresponding rapid decrease in resistance also occurs. Varistors are used to provide overvoltage protection in certain circuits.

Fig.2: Varistor I-V Curve

A thermistor is another special resistor. It is made of metallic oxides in a suitable binder and has a large negative coefficient of resistance (that is, resistance goes down with an increase in temperature). Figure 3 illustrates this resistance-temperature relationship.

Fig.3: Thermistor resistance-temperature relationship

The curve in figure 4 shows how the resistance changes with voltage for an incandescent lamp.

Fig.4: Incandescent Lamp I-V Curve

Figure 5 shows the I-V characteristic of a typical silicon diode.

Fig.5: Silicon Diode I-V Curve

The important thing to remember about any nonlinear resistance is that the resistance calculated for one value of V and I cannot be used when V and I change. But by making a number of changes in voltage and current, we can develop a resistance curve like the curves in above figures.